where we remind that \(\kappa _{\bullet ,\,\mathrm {H}\,\alpha }\)  is the opacity of the dust at H \(\alpha \)  as a cross-section per unit mass of dust.
We have defined in Section REF  the dust opacity as a cross-section per gram of gas as \(\kappa _{\mathrm {dust,\,H}\,\alpha }\equiv f_{\textrm {d/g}}\kappa _{\bullet ,\,\mathrm {H}\,\alpha }\)  and will use this below.
The dust-to-gas mass ratio is essentially zero at \(r<{R_{\textnormal {dest}}}\) ,
which is why the lower limit of the integration is the “dust destruction front” \({R_{\textnormal {dest}}}\)  [1]}.
From Equation (REF ), this is:
\({R_{\textnormal {dest}}}= \left(\frac{T_0}{{T_{\textnormal {dest}}}}\right)^2R_{\mathrm {p}}\) 
